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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Transition to collective oscillations in finite Kuramoto ensembles

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Peter, Franziska [1] ; Pikovsky, Arkady [1, 2]
Total Authors: 2
[1] Univ Potsdam, Inst Phys & Astron, Karl Liebknecht Str 24-25, D-14476 Potsdam - Germany
[2] Nizhnii Novgorod State Univ, Res Inst Supercomp, Gagarin Av 23, Nizhnii Novgorod 606950 - Russia
Total Affiliations: 2
Document type: Journal article
Source: Physical Review E; v. 97, n. 3 MAR 20 2018.
Web of Science Citations: 4

We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively. (AU)

FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
Grantee:Elbert Einstein Nehrer Macau
Support type: Research Projects - Thematic Grants